Abstract

This paper aims to clarify the conditions in which zero reflection from a dielectric film on metal substrate at oblique angles of incidence takes place. The numerical examples with experimental data show that the light absorption characteristics strongly depend on the film thickness. Therefore, it is useful to observe the oblique-incidence reflectance during the film deposition process for rapid and precise calibration of a thickness monitor.

© 1984 Optical Society of America

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References

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  1. H. Ishino, in Technical Digest, International Conference on Integrated Optics and Optical Fiber Communication (Tokyo, 1983), p. 292.
  2. J. Warner, “Faraday Optical Isolator/Gyrator Design in Planar Dielectric Waveguide Form,” IEEE Trans. Microwave Theory Tech. MTT-21, 769 (1973).
    [CrossRef]
  3. D. F. Horne, Optical Production Technology (Hilger, Bristol, England, 1983), p. 319.
  4. P. K. Tien, R. Ulrich, R. J. Martin, “Modes of Propagating Waves in Thin Deposited Semiconductor Films,” Appl. Phys. Lett. 10, 291 (1969).
    [CrossRef]
  5. H. Kitajima, K. Hieda, Y. Suematsu, “Thickness Measurement of Ultrathin Films on Metal Substrates Using ATR,” Appl. Opt. 19, 3106 (1980).
    [CrossRef] [PubMed]
  6. K. C. Park, “The Extreme Values of Reflectivity and the Conditions for Zero Reflection from Thin Dielectric Films on Metal,” Appl. Opt. 3, 877 (1964).
    [CrossRef]
  7. H. Kitajima, K. Hieda, Y. Suematsu, “Optimum Conditions in the Attenuated Total Reflection Technique,” Appl. Opt. 20, 1005 (1981).
    [CrossRef] [PubMed]
  8. Y. Suematsu, Y. Sasaki, H. Noda, E. Asai, M. Hakuta, “Measurements of Refractive Index and Film Thickness of Glass Films by Use of Propagation Constants,” Trans. IECE Jpn. 55-C, 98 (1972).

1981 (1)

1980 (1)

1973 (1)

J. Warner, “Faraday Optical Isolator/Gyrator Design in Planar Dielectric Waveguide Form,” IEEE Trans. Microwave Theory Tech. MTT-21, 769 (1973).
[CrossRef]

1972 (1)

Y. Suematsu, Y. Sasaki, H. Noda, E. Asai, M. Hakuta, “Measurements of Refractive Index and Film Thickness of Glass Films by Use of Propagation Constants,” Trans. IECE Jpn. 55-C, 98 (1972).

1969 (1)

P. K. Tien, R. Ulrich, R. J. Martin, “Modes of Propagating Waves in Thin Deposited Semiconductor Films,” Appl. Phys. Lett. 10, 291 (1969).
[CrossRef]

1964 (1)

Asai, E.

Y. Suematsu, Y. Sasaki, H. Noda, E. Asai, M. Hakuta, “Measurements of Refractive Index and Film Thickness of Glass Films by Use of Propagation Constants,” Trans. IECE Jpn. 55-C, 98 (1972).

Hakuta, M.

Y. Suematsu, Y. Sasaki, H. Noda, E. Asai, M. Hakuta, “Measurements of Refractive Index and Film Thickness of Glass Films by Use of Propagation Constants,” Trans. IECE Jpn. 55-C, 98 (1972).

Hieda, K.

Horne, D. F.

D. F. Horne, Optical Production Technology (Hilger, Bristol, England, 1983), p. 319.

Ishino, H.

H. Ishino, in Technical Digest, International Conference on Integrated Optics and Optical Fiber Communication (Tokyo, 1983), p. 292.

Kitajima, H.

Martin, R. J.

P. K. Tien, R. Ulrich, R. J. Martin, “Modes of Propagating Waves in Thin Deposited Semiconductor Films,” Appl. Phys. Lett. 10, 291 (1969).
[CrossRef]

Noda, H.

Y. Suematsu, Y. Sasaki, H. Noda, E. Asai, M. Hakuta, “Measurements of Refractive Index and Film Thickness of Glass Films by Use of Propagation Constants,” Trans. IECE Jpn. 55-C, 98 (1972).

Park, K. C.

Sasaki, Y.

Y. Suematsu, Y. Sasaki, H. Noda, E. Asai, M. Hakuta, “Measurements of Refractive Index and Film Thickness of Glass Films by Use of Propagation Constants,” Trans. IECE Jpn. 55-C, 98 (1972).

Suematsu, Y.

Tien, P. K.

P. K. Tien, R. Ulrich, R. J. Martin, “Modes of Propagating Waves in Thin Deposited Semiconductor Films,” Appl. Phys. Lett. 10, 291 (1969).
[CrossRef]

Ulrich, R.

P. K. Tien, R. Ulrich, R. J. Martin, “Modes of Propagating Waves in Thin Deposited Semiconductor Films,” Appl. Phys. Lett. 10, 291 (1969).
[CrossRef]

Warner, J.

J. Warner, “Faraday Optical Isolator/Gyrator Design in Planar Dielectric Waveguide Form,” IEEE Trans. Microwave Theory Tech. MTT-21, 769 (1973).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

P. K. Tien, R. Ulrich, R. J. Martin, “Modes of Propagating Waves in Thin Deposited Semiconductor Films,” Appl. Phys. Lett. 10, 291 (1969).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. Warner, “Faraday Optical Isolator/Gyrator Design in Planar Dielectric Waveguide Form,” IEEE Trans. Microwave Theory Tech. MTT-21, 769 (1973).
[CrossRef]

Trans. IECE Jpn. (1)

Y. Suematsu, Y. Sasaki, H. Noda, E. Asai, M. Hakuta, “Measurements of Refractive Index and Film Thickness of Glass Films by Use of Propagation Constants,” Trans. IECE Jpn. 55-C, 98 (1972).

Other (2)

D. F. Horne, Optical Production Technology (Hilger, Bristol, England, 1983), p. 319.

H. Ishino, in Technical Digest, International Conference on Integrated Optics and Optical Fiber Communication (Tokyo, 1983), p. 292.

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Figures (7)

Fig. 1
Fig. 1

Dielectric film on metal substrate structure.

Fig. 2
Fig. 2

Absolute values of Fresnel coefficients and normalized thickness vs incident angle for zero reflection, when the real part of complex refractive index n′ varies, |R12|, |R23|, and d0 vs θ1.

Fig. 3
Fig. 3

Normalized thickness vs the imaginary part of the complex refractive index for zero reflection, d0 vs n″.

Fig. 4
Fig. 4

Normalized thickness vs the refractive index of a dielectric film for zero reflection, d0 vs n2.

Fig. 5
Fig. 5

Reflectance vs incident angle, |R|2 vs θ1.

Fig. 6
Fig. 6

Reflectance vs normalized thickness |R|2 vs d0.

Fig. 7
Fig. 7

Reflectance vs normalized thickness for normal incidence: curve (1) Au substrate, curve (2) Si substrate; |R|2 vs d0.

Equations (7)

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R = R 23 exp [ i ( ϕ M - 2 ϕ d ) ] - R 12 1 - R 23 R 12 exp [ i ( ϕ M - 2 ϕ d ) ] ,
R 12 = | γ 1 - γ 2 γ 1 + γ 2 | ,
R 23 = | γ 2 - β M + i α M γ 2 + β M - i α M | ,
ϕ M = tan - 1 ( α M γ 2 - β M ) + tan - 1 ( α M γ 2 + β M ) ,
ϕ d = γ 2 d = 2 π n 2 d λ 0 cos θ 2 .
R 12 = R 23 ,
d λ 0 = ϕ M + 2 m π 4 π n 2 cos θ 2 ,             ( m = 0 , 1 , 2 , ) .

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